一类回归函数小波估计的相合性  

Consistency of Wavelet Estimators for a Family of Regression Functions

作　　者：寇俊克[1] 

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《北京工业大学学报》2015年第4期636-640,共5页Journal of Beijing University of Technology

基　　金：国家自然科学基金资助项目(11271038)

摘　　要：由于在实际应用中,回归函数的光滑性往往是未知的,假定回归函数的光滑性并不合理,因此研究一类带乘法噪声的回归模型,在不假定回归函数光滑性的条件下,证明了2种小波估计器的平均相合性.数值实验表明:随着样本容量的增大,由2种小波估计器得到的回归函数越来越接近真实的回归函数.特别地,当样本容量为1 000时,2种估计器得出的回归函数与真实回归函数基本吻合.数值实验支持了主要定理.该结论可看成是Chesneau与Shirazi工作的一种补充.Smoothness of the regression function is unknown in practical applications, so it isn＇t reasonable to assume the smoothness. This paper investigates a regression model based on size-biased random samples, and proves the mean consistency of two wavelet estimators without assuming any smooth conditions of the regression function. Numerical experiments indicate that regression functions given by the two wavelet estimators are closer to the true regression function as the size of sample increasing. Especially, they are almost same as the true regression function when the size of sample is 1 000. Numerical experiments support the main theorem. The results can be considered as a supplement of Chesneau and Shirazi＇s work.

关 键 词：小波估计 相合性 乘法噪声 

分 类 号：O174.2[理学—数学] O212.7[理学—基础数学]